Finite Group Databasebeta

← #18080291

Subgroups — #18080291

Order 4864.

726 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14567289C211yesmaximal, characteristic
2#14566221C211yesmaximal, characteristic, complemented
3#14562165C212yesmaximal
4#14561489C212yesmaximal, complemented
5C19×#1784C211yesmaximal, characteristic, complemented
6C2×#10597393C412yescomplemented
7C2×#10597376C2211yescharacteristic
8C2×#10597372—21no—
9#11926455—22no—
10#11926451—24no—
11#11926451C412yescomplemented
12#11926423—21no—
13#11926423—21no—
14#11926407—21no—
15#11926407C2212yes—
16C4×C22⋊Dic19C2211yescharacteristic
17#11926279—24no—
18C23×Q8×C19C2211yescharacteristic
19C2×C19×#101—22no—
20C19×#407C2212yes—
21C22×Q8×C19—22no—
22C22×Q8×C19—22no—
23C22×Q8×C19—44no—
24C22×Q8×C19C2×C412yes—
25C22×Q8×C19D412yes—
26C23×C4×C19D411yescharacteristic
27C23×C4×C19D411yescharacteristic
28C23×C4×C19C2311yescharacteristic
29C22×C22⋊D19—21no—
30C22×D76C2×C411yescharacteristic
31C2×M16×C19—22no—
32C2×C22⋊Dic19—21no—
33C2×C22⋊Dic19—22no—
34#10597393—44no—
35#10597376—22no—
36#10597376—22no—
37C2×(C2×D19)⋊C4—22no—
38C2×(C2×D19)⋊C4—22no—
39C2×(C2×D19)⋊C4—21no—
40#10597372—44no—
41C2×C4⋊Dic19—22no—
42C2×C4⋊Dic19C2×C411yescharacteristic
43C2×C4×Dic19—22no—
44C2×C4×Dic19C2×C412yes—
45C19×#101—44no—
46C19×C22⋊C8—22no—
47C19×C22⋊C8—22no—
48C19⋊#95—24no—
49C19⋊#95—22no—
50C19⋊#95—22no—
51C19⋊#95—21no—
52C19⋊#95—22no—
53C19⋊#95D414yes—
54C24×C19C2×D411yescharacteristic
55C23×D19—21no—
56C2×Q8×C19—24no—
57C2×Q8×C19—24no—
58C2×Q8×C19—24no—
59C2×Q8×C19—24no—
60C2×Q8×C19—42no—
61C2×Q8×C19—42no—
62C2×Q8×C19—44no—
63C2×Q8×C19—44no—
64C2×Q8×C19—48no—
65C22×C4×C19—21no—
66C22×C4×C19—21no—
67C22×C4×C19—24no—
68C22×C4×C19—21no—
69C22×C4×C19—21no—
70C22×C4×C19—42no—
71C22×C4×C19—42no—
72C22×C4×C19C22⋊C412yes—
73C22×C4×C19C22⋊C412yes—
74C22×C4×C19C22×C411yescharacteristic
75C22×C4×C19C2×D412yes—
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19#4112yes—
78C2×C22⋊D19—44no—
79C2×C22⋊D19—41no—
80C2×C22⋊D19—41no—
81C22×Dic19—22no—
82C22×Dic19—21no—
83C22×Dic19—24no—
84C2×D76—22no—
85C2×D76—42no—
86M16×C19—44no—
87C2×C8×C19—42no—
88C22⋊Dic19—42no—
89C22⋊Dic19—44no—
90(C2×D19)⋊C4—44no—
91(C2×D19)⋊C4—44no—
92(C2×D19)⋊C4—42no—
93C4⋊Dic19—22no—
94C4⋊Dic19—44no—
95C4×Dic19—44no—
96C4×Dic19—42no—
97#9466—191nomaximal, Sylow
98C23×C19—22no—
99C23×C19—22no—
100C23×C19—41no—
101C23×C19C2×C22⋊C411yescharacteristic
102C23×C19#12011yescharacteristic
103C23×C19#12311yescharacteristic
104C22×D19—42no—
105C22×D19—42no—
106C22×D19—41no—
107C22×D19—42no—
108Q8×C19—48no—
109Q8×C19—48no—
110C2×C4×C19—22no—
111C2×C4×C19—22no—
112C2×C4×C19—24no—
113C2×C4×C19—22no—
114C2×C4×C19—22no—
115C2×C4×C19—22no—
116C2×C4×C19—22no—
117C2×C4×C19—22no—
118C2×C4×C19—22no—
119C2×C4×C19—22no—
120C2×C4×C19—42no—
121C2×C4×C19—42no—
122C2×C4×C19—42no—
123C2×C4×C19—42no—
124C2×C4×C19#9914yes—
125C2×C4×C19C4×D412yes—
126C2×C4×C19#12112yes—
127C22⋊D19—82no—
128C22⋊D19—82no—
129C2×Dic19—44no—
130C2×Dic19—42no—
131C2×Dic19—44no—
132C2×Dic19—42no—
133C2×Dic19—42no—
134C2×Dic19—41no—
135C2×Dic19—42no—
136C2×Dic19—44no—
137D76—82no—
138C8×C19—82no—
139#2436—191no—
140#2310—191no—
141#1784D1911yescharacteristic, complemented
142#1510—192no—
143#1284—192no—
144C22×C19—21no—
145C22×C19—21no—
146C22×C19—21no—
147C22×C19—21no—
148C22×C19—21no—
149C22×C19—21no—
150C22×C19—21no—
151C22×C19—44no—
152C22×C19#38611yescharacteristic
153C22×C19C2×#9912yes—
154C22×C19#45412yes—
155C2×D19—84no—
156C2×D19—81no—
157C2×D19—81no—
158C2×D19—81no—
159C4×C19—22no—
160C4×C19—22no—
161C4×C19—24no—
162C4×C19—42no—
163Dic19—84no—
164Dic19—82no—
165Dic19—81no—
166C23×Q8C2×D1911yescharacteristic
167C2×#124—192no—
168C2×#121—191no—
169C2×#117—381no—
170C2×#101—22no—
171#407C2×D1912yes—
172#393—382no—
173#391—192no—
174#391—384no—
175#386—381no—
176#386—381no—
177#381—192no—
178#381—381no—
179C4×C22⋊C4—191no—
180#327—384no—
181C2×C19—22no—
182C2×C19—22no—
183C2×C19—41no—
184C2×C19#188811yescharacteristic
185C2×C19#189811yescharacteristic
186C2×C19#191211yescharacteristic
187D19—161no—
188C22×Q8—22no—
189C22×Q8—22no—
190C22×Q8—44no—
191C22×Q8C4×D1912yes—
192C22×Q8C22⋊D1912yes—
193C22×D4—191no—
194C22×D4—381no—
195C23×C4D7611yescharacteristic
196C23×C4D7611yescharacteristic
197C23×C4C22×D1911yescharacteristic
198C2×M16—22no—
199#124—764no—
200#121—382no—
201#121—382no—
202#117—764no—
203C2×C4⋊C4—191no—
204C2×C4⋊C4—382no—
205C2×C22⋊C4—382no—
206C2×C22⋊C4—381no—
207C2×C22⋊C4—382no—
208C2×C22⋊C4—382no—
209C2×C22⋊C4—381no—
210C2×C42—192no—
211C2×C42—382no—
212#101—44no—
213C22⋊C8—22no—
214C22⋊C8—22no—
215#95—194no—
216#95—384no—
217#95—382no—
218#95—382no—
219#95—382no—
220#95—381no—
221C19#946611yescharacteristic, complemented, Sylow
222C24—381no—
223C24C2×D7611yescharacteristic
224C2×Q8—24no—
225C2×Q8—24no—
226C2×Q8—24no—
227C2×Q8—24no—
228C2×Q8—42no—
229C2×Q8—42no—
230C2×Q8—44no—
231C2×Q8—44no—
232C2×Q8—48no—
233C2×D4—382no—
234C2×D4—762no—
235C2×D4—764no—
236C2×D4—761no—
237C2×D4—761no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—24no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—384no—
246C22×C4—381no—
247C22×C4—382no—
248C22×C4(C2×D19)⋊C412yes—
249C22×C4(C2×D19)⋊C412yes—
250C22×C4C2×C4×D1911yescharacteristic
251C22×C4D4×D1912yes—
252C22×C4#6454312yes—
253C22×C4C2×C22⋊D1911yescharacteristic
254M16—44no—
255C2×C8—42no—
256C4⋊C4—382no—
257C4⋊C4—764no—
258C22⋊C4—764no—
259C22⋊C4—762no—
260C22⋊C4—764no—
261C22⋊C4—762no—
262C22⋊C4—764no—
263C42—762no—
264C42—764no—
265C23—22no—
266C23—22no—
267C23—41no—
268C23—762no—
269C23—762no—
270C23—761no—
271C23—762no—
272C23#1059732811yescharacteristic
273C23#1059733211yescharacteristic
274C23C2×(C2×D19)⋊C411yescharacteristic
275Q8—48no—
276Q8—48no—
277D4—1522no—
278D4—1522no—
279D4—1522no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—24no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—764no—
295C2×C4—762no—
296C2×C4—762no—
297C2×C4—764no—
298C2×C4—762no—
299C2×C4—761no—
300C2×C4—764no—
301C2×C4—762no—
302C2×C4#1059726314yes—
303C2×C4(C22⋊D19)⋊C412yes—
304C2×C4#1059738512yes—
305C8—82no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—44no—
314C22—1524no—
315C22—1521no—
316C22—1521no—
317C22—1521no—
318C22#1192642111yescharacteristic
319C22C2×#1059726312yes—
320C22#1192671912yes—
321C4—22no—
322C4—24no—
323C4—22no—
324C4—42no—
325C4—1524no—
326C4—1522no—
327C4—1521no—
328C2—22no—
329C2—22no—
330C2—41no—
331C2—3041no—
332C2#1456403611yescharacteristic
333C2#1456408611yescharacteristic
334C2#1456417011yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1784C2
socleC22×C19#386
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1784D19
hypocenterC19#9466
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1784

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14566221C2semidirect
4. #14561489C2semidirect
5. C19×#1784C2semidirect
6. C2×#10597393C4semidirect
11. #11926451C4semidirect
141. #1784D19semidirect
221. C19#9466semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145672892
#145662212
#145621652
#145614892
C19×#17842
#946619